1. **State the problem:** We need to find how long it will take for two pumps working together to empty a tank if the first pump takes 11 hours alone and the second pump takes 20 hours alone. 2. **Define rates:** - Pump 1 rate is $\frac{1}{11}$ tanks per hour. - Pump 2 rate is $\frac{1}{20}$ tanks per hour. 3. **Add rates:** The combined rate when both pumps work together is $$\frac{1}{11} + \frac{1}{20} = \frac{20}{220} + \frac{11}{220} = \frac{31}{220}$$ tanks per hour. 4. **Find total time:** To find total time $t$ when both pumps work simultaneously, use $$t = \frac{1}{\text{combined rate}} = \frac{1}{\frac{31}{220}} = \frac{220}{31} \approx 7.09677$$ hours. 5. **Interpretation:** This means both pumps together take approximately $7.096$ hours to pump out the tank. 6. **Final answer:** The closest option is (b) 7.096 hours.